A simplified version of the expression 2sinθ (cos θ)(cotθ) is
as was already posted,
2cos^2 θ
To simplify the expression 2sinθ (cos θ)(cotθ), we'll first use trigonometric identities to simplify each term individually.
Let's start with the term 2sinθ. This can be written as 2sinθ(1) since we know that multiplying by 1 doesn't change the value. Therefore, the term 2sinθ simplifies to just 2sinθ.
Next, let's consider the term (cosθ). This is already simplified since there are no other factors to simplify it further.
Finally, let's simplify the term (cotθ). Cotangent can be defined as the reciprocal of tangent, so cotθ is equal to 1/tanθ.
Now, we can rewrite our expression as 2sinθ (cos θ)(1/tanθ).
To simplify further, we can cancel out common factors between sinθ and cosθ. We know that sinθ/cosθ is equivalent to tanθ, so we can rewrite the expression as 2(tanθ)(1/tanθ).
Now, we can cancel out the common factor of tanθ, leaving us with just 2(1), which simplifies to 2.
Therefore, the simplified version of the expression 2sinθ (cos θ)(cotθ) is 2.